We claim that momentum is conserved, yet:f3 8f oyf1t34kkhn ical8y/y most moving objects eventually slow down and stopyht/: ck8kyy3nf ao18 3if4l f. Explain.

When a person jumps from a tree to the grou v 4i-acrl.7 mcyc9(w9myz)6pw yjik 6nd, what happens to the momentum of the person upc)myk9wa- c ir6m .v79z6cjyyli4 pw(on striking the ground?

When you release an inflated but untied balloon, why p6 mj/ctqj r ;kpn,*gw.*;g8b gppn a/does it fly across the room?;ntk,*nc6jgpp ;ab.rg q/ p g/w8*pjm

It is said that in ancient times a rich man with a bag omqgo6 h. i(oo n3piq6f1s5sy,thx 74b f gold coins froze to death while strandedh.7o,ng4qqxi3 b(o1 5myf6hisstop 6 on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentj0gyj-,e.jik,e5 hkbn/o6abk f k x*4ially in a vacu b-kk egaif *jxk/ jo6jn5,bkh4e0y ,.um?

According to Eq. 7–5, the longer the q hibn qv ,;nhr1n18dz o6y-.tc lq47eimpact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision a l 8qbvr, n7qz e1d.1n-q;thnc46iyohnd reduce the possibility of fracture or death.

Cars used to be built as rk ,4)49shex kdga0mf sigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zonfehxmkkd,0 )449sgas es” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in: w:bb tmjt90r the air by tmr b:: 9wb0jtthe batter?

Is it possible for an object to receive a larger impulse from a sm 4w8pty /wku764mkw mifr*zj4all force than from a large force? Exp/ku4y 7i kw8tm zw44fm6jrp* wlain.

A light object and a heavy object have the same kinetic energy. Which has p/ r2 opvxq1rwum*v .tnz)1; rvppe .2the greater momentum? Explai r;e.* prv 11vv/p.2pxzmqnutrpw)o2 n.

Describe a collision in w/ k4mknl yfr83hich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high spe0+m e(aa oy4sjm-tuw)ed against turbine blades on an axle that turns an electric generator. Foe m4uys om+jt0w(a a-)r maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall 1em nmg4chjb: )rmwm- 6rso :/o2um+ dli) bk9at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped fromv;* yp/xa.y ;zq pjc ,qb z3b8)(jtbjx a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its originalpz *qj;b)vb. bqt/;p( jy3 jyx,xca8z speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carryin ukck45ag6e2ag a heavy load in your arms?

Why is the CM of a 1-m length of.j o*lspkmm ib7*; )kz pipe at its mid-point, whereas this is not true for your arm or le.*ms k*oml) bpki;z7 jg?

Show on a diagram how your CM shifts when you change from a lying posi)pej1uxj- p f3tion to a sitting poxu 31jj)pefp-sition.

If only an external force can change the momentum of the center of mass of an obon5r r:5d;olb h 1h3luos7d.b jlt.0qject, how can the internal force of an engine accelerate a ca ro.bbd5 lo ;7 l1.tuhor3:sl05q hndjr?

A rocket following a parabolic path through the air suddenly explodes into manyezh5sbh-ps 6(v b ip3p)eum )6 pieces. What can you say about the motionshphe )6bep)ui p-(m s53bz6v of this system of pieces?

  What is the magnitude of the momentum vnf/ j* zdsi2tpzrz x 3x88ozx+fux)8wc *v+6of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 2m7v6iilfwn ;x gy,ay7ge 8 +)d5 N acts on a 65-kg skier for 20 s. What is the skier’s changeei,mi7d;7vw nya+ fgg)y86xl in velocity?    m/s

  A 0.145-kg baseball pitchev6j 5 zgqs lnc*.2,zhkl/tcv /d at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s c6 /*n,j/hlgvs 2lkqt5 cz. zvIf the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out hodze6c b ;7 8drk/tbuy bvyub9 vl-s-0*rizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was d6bl0z bcv/uvrd 7;8t9- *yb kesu-by initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the prop q0lc k7 qfab -r,irb84il/0xwelling gases are expelled at a rate oblfiir0wqc 8 a0-kqrx ,lb/4 7f $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at 4lv ozv 9 ad7nwm,rc8k/k -fz8$4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car tt,f2ujpf6i 6 oravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped ontuo6, f26fpit jo the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelicskye,k. (u k8ng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, win9p0oi rby g+vcru.g9: ds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assum99pigu g+ :0y.ovcb rre the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant5j 37hd/tnivc0s)/*axxvnn8 ko/u c e speed of 8.6m/s on a level track. Snntu/jxv/xnak*e038 hv)d/5oi7nc c sow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emitx5p72wgzrg:x 31jn( c9p liocj*p 5 kks an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u2 g5p 5 jcgr3xk (x1j7zlpkn9c *oiw:p and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block ofy 60vz cy59fg/2yrhu. a4j4 uh/n jngj wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surfac/y4hr0 gj6cjyguay9fvn 25h uzn.j /4e when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket istkon/4 qx7f 0w traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass0 f wqz2o*drj3i/ agf9 3180 kg is traveling in outer space with a velocity of 115ma *d2r9io /0zfjw 3qfg/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the th jqvz6t;(l.9stt cnkx- a/ u3ee at a speed of 45m/s The golf club was in contact with the ballstnvu 6.lk9; jhc-z t(a3q /xt for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest in a t3mkib4wgsq31 -426c kr abk ayime interval of 8.0 ms. (a) What is the impulse 24b3sk-w3imkr aa ckb4yg1q 6given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wkubyt r4y(l.j)q(. h ball at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthinessv7x4r .6kkan o of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). v7o.6 x4r aknkA new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s 3gwr8-e 4 *gmrt myu9pto the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west p*g-tymr8eu943gr mw. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x dire1( c,ybbl*isavod :u *ction and is given by the graph of Fig. 7–33 a bsdi o:ly,*b(1vcua *s a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower leg wv-q:3q kwbs5bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in b-3:k5vswq wqb reaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of n b8yuio3(/x 1jop )bgcollides head-on with a 0.220-kg ball1 y3j)o(bg x/i 8bpuon at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a h,rt odbnpidan87 9e9 45u;vmr0pg:iw ead-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collisiond aur89etid;gnnv 0br 7o5,p9:imp 4w?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a pe 1qc52 v*oevvxrfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball 1o qv25v exvc*moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides he+, )ta2 -qfqknk r6udtad-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s -auk,+tk q6ndfr2)tq Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.22de1e he+ i(xltu 1s;ri 6t/s)x0 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initiall)s u t+i 1elx d16rsei;/xeh(ty at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide e (avqz::k2ahys 3d v-r4z 6doklastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger masdh:v zv2d qk6yo - as(rz4k:3as. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elax6ga -cw82okyl w j5i.stic head-on collision with a second ball initially at rest. The second ball moves off with half the originagij w28w yo-c5x. alk6l speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionll xh;ycwwt.i :q4v:h.ess incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only oq:hl wt4v.c ; :hixwy.ne-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objexxe8ecpwmz :a 1d6h15 to 66fvct of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experimens-qiq y 2kn/m5t, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectis-nq2q/ k5myi le causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hang3,lxov4 0o pxfing on a 2.8-m-lon 0vo3l,4xxfo pg string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetice3 :i vks(cw.uluh5.)jada9 t energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two p y0uof-90iq6b*x,(j xm( +vhyfewb- cxrims (ieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the yxumjf 0sf9(x-bch+veix0 qri((*- y 6w bm, olighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV st/ 8h(pljk)gk jopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports ca pk(/ g)ljkhj8r at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 mr tvzk8.m/d 7f and rebounds to a height of 1.20 m. Approximat d/7t.mrz kfv8ely how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticit+*b2ro5zl sz-mk(lmfy in a head-on collision of two objects is the coefficient of restitution, e, defined a+( mzzf m2blk*sl-5ros$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times 4u n3/nt7piawthe mass of the other. A depres/w3n 74una itpsion is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wm y )vymx9gbb -(8jl h1nr-1gkith a 10.gl kb1 ( yx9g-rm h)81jv-nymb0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a sec 1ezw(5of3 kr1y1e tbdond nucleus, an electron, and a neutrino. The electron and neutrino are emitted b1 ety1dozr( ew3 k15fat right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masse 0*af.a prumi4hsz61z,/ckpxb zf 8/ $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two ts1z. /5k7aoko(.ofto p6)lu9b ru p lobjects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initk/. f7)usaorz9utt1l o (6 lboo.pk p5ial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and mee4hr7lbss8,qo( mej )4x 3ulkg7l f;wwt at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along thf lr k7w73h4,s lwebu;8m oqxgjs4()le positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfect0y)) *am,lcb0e9sd-x4a.5fao l ,uoplljw vvly elastic collision with another atom at rest. Afta0aao ocl-b,x9*0 lvpw fuj )ls 4v.ey5,md)ler the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfec3tazlx tly 96uzn5 6)gtly elastic collision with another atom at rest. After the impact, the neongxtaz9l3 65lnzu6y)t atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of t;i tsllh*3wiv+8qco:i*u4mc he three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mqvci;wlu**th43c o+:smi il 8ass.    m

  The distance between a carbon atom) *p 6ld6e6mmt guydl 2gc:cn4 ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of1j;u- d*g-sl tjmjs3uwg 3r +l the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the froug3+; lr-ls*jg sj tdm13jwu-nt? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass / wsb-md2,gpo o/yv) sf4r la46800 kg, is used as a ferryboat. If three cars, each of m4 p blo m,2so)ary4g- fwsvd//ass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side u/6a)ln d 0q3ksf5xvqs $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identic rf -h2movbv t2f,4)ayal cases of tomato paste (see Fig. 7–40), each of which is a cube of lengvh 24bt2 fy -vm)r,foath l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut out o;tbpd9fe6l;joa8t j( f it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subt( ;tde; a96tolj8jbfpraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculate ts-avwk2/s m x*mdp 4*ghe mass of one of your le v- /dk* wsg*mmxsp24ags.    kg

  Determine the CM of an outstretched a 5sd zz*w.p,t6pz5b6ef sd(h;9gnpdtrm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CMu2+l ir 2ktf q0tddy4) of an arm bent at a right angle. Assume that the person is qu0 2y)did 2+tk4ftlr155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are han -t6fywt8qvt4.x .ezx+7cez2w bmk8oging vertically, and his trunk and head wy.8+e.e 4 zv68mtco t-t 2xwqb zkfx7are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon arepcj/0* wd22a*tt oncvbp,z 0c $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frict8ixc1 +am4;uukszy-t ionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of masbikmb- 84 s,wnhsz 7e*s 2.00 kg and a diameter 0.0800 m mounteks*7- si eh, n4zbbm8wd on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindricmp. /: d9zr/vehg+psq al head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that wil9mrpg/hp+sd. :/zqv el follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 r.at8zlpwx/mc/ ql81 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola,*-kya fhaz,r , ipc37l of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happ-z*,hkarc,7fy 3 lpiaens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at /3nt ovd6ix+l strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is x+nv 36/toid l1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withbrai(mx7 i+ yj;0 fuo1 speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced wi8 6e af-xn)hfhth the corner pocket shot shown in Fig. 7–43. Relfa6nh 8ex-)fh ative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speeda*r+wx c 3zu2-odz78xd mk xm6 of 2.5m/s by pushing off with his legs from an 1800-kg space x82u *3 ox az 76zkrxw-cdmm+dcapsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and thes 0:cqkj o/1bi other 80 kg, are initially at rest in outer space. They then push each other apart. How far aksq01 jci b:/opart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a smlt41bpw6( cgwvo6/c0 2 be msecond ball (at rest) and rebounds in the opposite direction1w( e20 wvt /g6obmp6mc4clsb with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an autoxeemb*p8ftq e6c +q;6 mobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic pe;x bf6 6 emqtqec*8+friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the z-qnb+j5rt)yfz--r96g/d rswnt ,qv top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizon5 b-dts9-qnqjz-r rz)tw g6vf ny/r+,tal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block :awy tj-qk+j(o0u+xc u x 0ni+of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in iu0i+xt(yno xc0w+ +qk jaj:-ut?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg blevmf ,y6u) cv(0;ay4 skpfe q,ock of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is, ,0sevyfy )eu;4(pq kfc6amv 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboag ipm93sh46 ;jp wxpd0t of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in whatd pi;s436px gm9w0pjh direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa rg5b( bubzj4xnc e:8t)l85evs about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart int)f, oftzzv:gysrb+4/;dw d o2o two fragments by an explosion. One fragmenttwydf:dg+,2f/z z ) rbsvo4;o acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-( .i )c0ykju jq7$1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses)8ix bc l96tft $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an8d) 0bix xa 5vdovmqzbfu3a9 )m;(9 md alpha particle and a smaller nucleus. What will be the speed of this recoil0bdmz 8f)3a5db ma)uqm;d9ivvo x(9x ing nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle8,h 4 2wsxx5k8fuz6 vc 7lguhx of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slide r43poqw 94m 3yczxm1s7ohs )rs down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the uppya)qyfw 8l.+m5ij wr+z au87yer limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and c+f5yw)jl .a yu a+wqz7i8rym8ollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 show5ry-u* v2hlrx) pv ea3u0q//ud q5gyss the planet Saturn moving in the negative x direction at its orbital u hlydu2a-r5s5yg/u)/vq0*p qvxre3 speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s